Introduction To Quaternions With Examples Etc
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Introduction To Quaternions With Examples Etc
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Author : Philip KELLAND (and TAIT (Peter Guthrie))
language : en
Publisher:
Release Date : 1873
Introduction To Quaternions With Examples Etc written by Philip KELLAND (and TAIT (Peter Guthrie)) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1873 with categories.
Understanding Quaternions
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Author : Peng Du
language : en
Publisher: Nova Science Publishers
Release Date : 2020
Understanding Quaternions written by Peng Du and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
"Quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. They form an interesting algebra where each object contains 4 scalar variables, instead of Euler angles, which is useful to overcome the gimbal lock phenomenon when treating the rotation of objects. This book is about the mathematical basics and applications of quaternions. The first four chapters mainly concerns the mathematical theories, while the latter three chapters are related with three application aspects. It is expected to provide useful clues for researchers and engineers in the related area. In detail, this book is organized as follows: In Chapter 1, mathematical basics including the quaternion algebra and operations with quaternions, as well as the relationships of quaternions with other mathematical parameters and representations are demonstrated. In Chapter 2, how quaternions are formulated in Clifford Algebra, how it is used in explaining rotation group in symplectic vector space and parallel transformation in holonomic dynamics are presented. In Chapter 3, the wave equation for a spin 3/2 particle, described by 16-component vector-bispinor, is investigated in spherical coordinates. In Chapter 4, hyperbolic Lobachevsky and spherical Riemann models, parameterized coordinates with spherical and cylindric symmetry are studied. In Chapter 5, ship hydrodynamics with allowance of trim and sinkage is investigated and validated with experiments. In Chapter 6, the ballast flying phenomenon based on Discrete Discontinuous Analysis is presented. In Chapter 7, a numerical study is proposed to analyze the effect of the caisson sliding subjected to a hydrodynamic loading in the stability of the rear side of the rubble mound breakwater"--
Visualizing Quaternions
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Author : Andrew J. Hanson
language : en
Publisher: Elsevier
Release Date : 2006-02-06
Visualizing Quaternions written by Andrew J. Hanson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-06 with Mathematics categories.
Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. - Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. - Covers both non-mathematical and mathematical approaches to quaternions.
Lessons In Elementary Mechanics Introductory To The Study Of Physical Science Etc
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Author : Sir Philip MAGNUS
language : en
Publisher:
Release Date : 1875
Lessons In Elementary Mechanics Introductory To The Study Of Physical Science Etc written by Sir Philip MAGNUS and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1875 with categories.
Vector Analysis And Quaternions
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Author : Alexander Macfarlane
language : en
Publisher: HOLISTENCE PUBLICATIONS
Release Date : 2024-03-14
Vector Analysis And Quaternions written by Alexander Macfarlane and has been published by HOLISTENCE PUBLICATIONS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-14 with Antiques & Collectibles categories.
Quaternionic Integral Transforms
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Author : Eckhard Hitzer
language : en
Publisher: Springer Nature
Release Date : 2023-08-08
Quaternionic Integral Transforms written by Eckhard Hitzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-08 with Mathematics categories.
This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book’s editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.
Topics In Quaternion Linear Algebra
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Author : Leiba Rodman
language : en
Publisher: Princeton University Press
Release Date : 2014-08-24
Topics In Quaternion Linear Algebra written by Leiba Rodman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-24 with Mathematics categories.
Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.
An Introduction To Abstract Algebra
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Author : F. M. Hall
language : en
Publisher: Cambridge University Press
Release Date : 1972-04-06
An Introduction To Abstract Algebra written by F. M. Hall and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-04-06 with Mathematics categories.
This two-volume course on abstract algebra provides a broad introduction to the subject for those with no previous knowledge of it but who are well grounded in ordinary algebraic techniques. It starts from the beginning, leading up to fresh ideas gradually and in a fairly elementary manner, and moving from discussion of particular (concrete) cases to abstract ideas and methods. It thus avoids the common practice of presenting the reader with a mass of ideas at the beginning, which he is only later able to relate to his previous mathematical experience. The work contains many concrete examples of algebraic structures. Each chapter contains a few worked examples for the student - these are divided into straightforward and more advanced categories. Answers are provided. From general sets, Volume 1 leads on to discuss special sets of the integers, other number sets, residues, polynomials and vectors. A chapter on mappings is followed by a detailed study of the fundamental laws of algebra, and an account of the theory of groups which takes the idea of subgroups as far as Langrange's theorem. Some improvements in exposition found desirable by users of the book have been incorporated into the second edition and the opportunity has also been taken to correct a number of errors.
Life Of Sir William Rowan Hamilton Knt Ll D D C L M R I A Andrews Professor Of Astronomy In The University Of Dublin And Royal Astronomer Of Ireland Etc Etc
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Author : Robert Perceval Graves
language : en
Publisher:
Release Date : 1889
Life Of Sir William Rowan Hamilton Knt Ll D D C L M R I A Andrews Professor Of Astronomy In The University Of Dublin And Royal Astronomer Of Ireland Etc Etc written by Robert Perceval Graves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1889 with Quaternions categories.
Historic Magazine And Notes And Queries
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Author :
language : en
Publisher:
Release Date : 1882
Historic Magazine And Notes And Queries written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1882 with categories.
List of bibliographies and trans. in v. 1-12.